???????????? ?????? ? ????? ??????? ???????????? ??????????? �????????? ???????????� / ???? ? ???????????? ?????? ?2 ? ??????????: �?????????? ?? ??????????? ??????????� ??????? 14  ???? ??????: ??????? ?????? ???????????? ?????. ?????? ??????? ????�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� N; ???????
; ???????-???????
. ?? ????????? ??????? ????????? ? ??????????, ??? ???????????? ?????????? ????? (???? ???????????). ??? ????, ???????? ???? ??????? ?? ???????? ? ?????? ????????? ???????, ???????? ?? ????. ??????-???????? ?? ??????? ?????????????, ???????? ? ???????? ???????????. ??????? C2 ??????? ???????????? ?? ????????: Cij=14/(i+j4) ?????? ???????? b ??????? ???????????? ?? ????????: bi=14/(i3) � ??? ?????? ? bi=1/(i+14) � ??? ???????? ? ????????????/ ???.1. ???????????? y1 - ????????? ???????? ??????? ? ?? ??????-???????? b ? ??????-????????. y2 - ??????????? ???????? ??????? ?1 ?? ??????-???????? �14b1+14c1� ? ??????-????????. Y3 - ??????????? ???????? ??????? ?? ??????? ? ???????, ?? ??? ????????? ??????? ??????????? ???? ????? ???????. Y3^3 - ??????? y2y1� � ??????? y2�Y3 � ????? y2�Y3y1 � ????? y2�Y3y1Y3 - ??????? Y3^3y1y1� � ??????? Y3^3y1y1�+ y2y1�+ y2�Y3y1Y3 � ??????? ????????? ?????? ??? ?????????? MPI ????? ?????? ????? ??????? ??????? ?? ???????? ?? ?????? ? ???????? ??????? ?? ???????? N = 2 ?? ??????? ??????????? ?? ????? ?? ? ????, ????????? ???????? 3. ???????? ???????????? ? ?????????. / / / / ???.2.1 ?? 2.2. ?????????? ?????? ??????? ????????? ? Matlab (???? ??????) ??????? ???????? ?? ???????: i = 1 j = 1 bi = zeros(2,1) Cij = zeros(2,2) A2 = [2 2; 2 2] B2 = [2 2; 2 2] A = [2 2; 2 2] A1 = [2 2; 2 2] b1 = [2; 2] c1 = [2; 2] while i<=2 if(mod(i,2) == 0) bi(i)=14/(i*i*i) else bi(i)=1/(i+14) end i=i+1 end i=1 j=1 while i<3 while j<3 Cij(i,j)=14/(i+j*j*j*j) j=j+1 end j = 1 i=i+1 end y1 = A*bi y2 = A1*((14*b1)+(14*c1)) Y3 = (A2*Cij)-B2 res1 = Y3*Y3*Y3*y1*y1' res2 = y2*y1' res3 = y2'*Y3*y1*Y3 X = res1 + res2 + res3 ????????? ?????????: i = 1 j = 1 bi = 2�1 0 0 Cij = 2�2 0 0 0 0 A2 = 2�2 2 2 2 2 B2 = 2�2 2 2 2 2 A = 2�2 2 2 2 2 A1 = 2�2 2 2 2 2 b1 = 2�1 2 2 c1 = 2�1 2 2 bi = 2�1 0.0667 0 i = 2 bi = 2�1 0.0667 1.7500 i = 3 i = 1 j = 1 Cij = 2�2 7 0 0 0 j = 2 Cij = 2�2 7.0000 0.8235 0 0 j = 3 j = 1 i = 2 Cij = 2�2 7.0000 0.8235 4.6667 0 j = 2 Cij = 2�2 7.0000 0.8235 4.6667 0.7778 j = 3 j = 1 i = 3 y1 = 2�1 3.6333 3.6333 y2 = 2�1 224 224 Y3 = 2�2 21.3333 1.2026 21.3333 1.2026 res1 = 2�2 105 � 1.5109 1.5109 1.5109 1.5109 res2 = 2�2 813.8667 813.8667 813.8667 813.8667 res3 = 2�2 105 � 7.8256 0.4411 7.8256 0.4411 X = 2�2 105 � 9.3446 1.9602 9.3446 1.9602 ????? ????? 0.txt: N = 2.000000 Cij = 7.000000 0.823529 4.666667 0.777778 bi = 0.066667 1.750000 c1 = 2.000000 2.000000 A2 = 2.000000 2.000000 2.000000 2.000000 B2 = 2.000000 2.000000 2.000000 2.000000 A1 = 2.000000 2.000000 2.000000 2.000000 A = 2.000000 2.000000 2.000000 2.000000 b1 = 2.000000 2.000000 A2*C2 = 23.333332 3.202614 23.333332 3.202614 Y3 = 21.333332 1.202614 21.333332 1.202614 Y3^2= = 480.766815 27.102053 480.766815 27.102053 Y3^3= = 10834.535156 610.770386 10834.535156 610.770386 y2y1' = = 813.866699 813.866699 813.866699 813.866699 y2'Y3y1Y3 = = 782560.187500 44114.914062 782560.187500 44114.914062 Y3^3y1y1' = = 151090.765625 151090.765625 151090.765625 151090.765625 X = 934464.812500 196019.531250 934464.812500 196019.531250 ????? ????? 1.txt: N = 2.000000 b1 = 2.000000 2.000000 c1 = 2.000000 2.000000 14 * b1 + 14 * c1 = 56.000000 56.000000 A1 = 2.000000 2.000000 2.000000 2.000000 y2= = 224.000000 224.000000 y1= = 3.633333 3.633333 y2y1' = 813.866699 813.866699 813.866699 813.866699 y2'Y3 = 9557.333008 538.771240 y2'Y3y1 = 36682.511719 y2'Y3y1Y3' = 782560.187500 44114.914062 782560.187500 44114.914062 ????? ????? 2.txt: N = 2.000000 bij = = 0.066667 1.750000 y1=A*bi = 3.633333 3.633333 Y3^3 = 10834.535156 610.770386 10834.535156 610.770386 Y3^3y1 = 41584.613281 41584.613281 Y3^3y1y1' = = 151090.765625 151090.765625 151090.765625 151090.765625 y2'Y3 = 9557.333008 538.771240 y2'Y3y1 = 36682.511719 ????? ????? consistent.txt: N = 2.000000 Cij = 7.000000 0.823529 4.666667 0.777778 bi = 0.066667 1.750000 c1 = 2.000000 2.000000 A2 = 2.000000 2.000000 2.000000 2.000000 B2 = 2.000000 2.000000 2.000000 2.000000 A1 = 2.000000 2.000000 2.000000 2.000000 A = 2.000000 2.000000 2.000000 2.000000 b1 = 2.000000 2.000000 A2*C2 = 23.333332 3.202614 23.333332 3.202614 Y3 = 21.333332 1.202614 21.333332 1.202614 Y3^2= = 480.766815 27.102053 480.766815 27.102053 Y3^3= = 10834.535156 610.770386 10834.535156 610.770386 14 * b1 + 14 * c1 = 56.000000 56.000000 y2= = 224.000000 224.000000 y1=A*bi = 3.633333 3.633333 y2y1' = 813.866699 813.866699 813.866699 813.866699 y2'Y3 = 9557.333008 538.771240 Y3^3y1 = 41584.613281 41584.613281 Y3^3y1y1' = = 151090.765625 151090.765625 151090.765625 151090.765625 y2'Y3y1 = 36682.511719 y2'Y3y1Y3' = 782560.187500 44114.914062 782560.187500 44114.914062 X = 934464.812500 196019.531250 934464.812500 196019.531250 ????? ???????? (MPI) Header.h: #pragma once #include #include #include #include "math.h" #include #include #include using namespace std; //Operations float** dobytok_2_matruc(int rozmir, float** matrix1, float** matrix2); float** dobytok_matrix_vectorStovpec(int rozmir, float** matrix, float** vector); float* dobytok_vectorRjadok_matrix(int rozmir, float** matrix, float* vector); float** transp_vectorRjadka(int rozmir, float** vector); float* transp_vectorStovpcja(int rozmir, float** vector); float dobytok_Rjadka_na_Stovbec(int rozmir, float** vectorS, float* vectorR); float** dobytok_Stovbec_na_Rjadok(int rozmir, float** vectorS, float* vectorR); float** dobytok_chislo_na_Stovbec(int rozmir, float number, float** vectorS); float** dobytok_chisla_na_matrix(int rozmir, float numb, float** matrix); //initialization void vector_Column(float**& V, int size); void vector_Row(float*& V, int size); void matrix(float**& M, int size); void number(float**& Numb); //file void write_to_file(ofstream& fx, float** MRC, int N, int processor, char whatIs, char* name); void write_to_file_ROW(ofstream& fx, float* MRC, int N, int processor, char* name); //???????? ????? ????????? ?? ??????? void write_to_file1(ofstream& fx, float MRC, int N, int processor, char* name); //input void manual_input(int& N, float**& C, float**& b, float**& c1, float**& A2, float**& B2, float**& A1, float**& A, float**& b1); void auto_input(int& N, float**& C, float**& b, float**& c1, float**& A2, float**& B2, float**& A1, float**& A, float**& b1); void CPU_0(); void CPU_1(); void CPU_2(); WtFile.cpp: #include "Header.h" void write_to_file(ofstream& fx, float** MRC, int N, int processor, char whatIs, char* name) { fx.setf(ios::fixed); const char* path; if (processor == 0) path = "D:\\0.txt"; else if (processor == 1) path = "D:\\1.txt"; else if (processor == 2) path = "D:\\2.txt"; else { cout << "Error: bad processor = " << processor << endl; path = "D:\\Error.txt"; } if (whatIs == 'M') { fx.open(path, std::ofstream::out | std::ofstream::app); fx << name << " = \r\n"; for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { fx.width(10); fx.fixed; fx << MRC[i][j] << "\t"; } fx << "\r\n"; }fx << "\r\n\n\n"; fx.close(); } else if (whatIs == 'R') { fx.open(path, std::ofstream::out | std::ofstream::app); fx << name << " = \r\n"; for (int i = 0; i < N; i++) { fx.width(10); fx.fixed; fx << MRC[0][i] << "\t"; } fx << "\r\n\n\n"; fx.close(); } else if (whatIs == 'C') { fx.open(path, std::ofstream::out | std::ofstream::app); fx << name << " = \r\n"; for (int i = 0; i < N; i++) { fx.width(10); fx.fixed; fx << MRC[i][0] << "\r\n"; }fx << "\r\n\n\n"; fx.close(); } else if (whatIs == 'N') { fx.open(path, std::ofstream::out | std::ofstream::app); fx << name << " = " << MRC[0][0] << "\r\n"; fx.close(); } else { cout << "Error: bad type to write into file, proc = " << processor << endl; } } void write_to_file_ROW(ofstream& fx, float* MRC, int N, int processor, char* name) { fx.setf(ios::fixed); const char* path; if (processor == 0) path = "D:\\0.txt"; else if (processor == 1) path = "D:\\1.txt"; else if (processor == 2) path = "D:\\2.txt"; else { cout << "Error: bad processor = " << processor << endl; path = "D:\\Error.txt"; } fx.open(path, std::ofstream::out | std::ofstream::app); fx << name << " = \r\n"; for (int i = 0; i < N; i++) { fx.width(10); fx.fixed; fx << MRC[i] << "\t"; } fx << "\r\n\n\n"; fx.close(); } void write_to_file1(ofstream& fx, float MRC, int N, int processor, char* name) { fx.setf(ios::fixed); const char* path; if (processor == 0) path = "D:\\0.txt"; else if (processor == 1) path = "D:\\1.txt"; else if (processor == 2) path = "D:\\2.txt"; else { cout << "Error: bad processor = " << processor << endl; path = "D:\\Error.txt"; } fx.open(path, std::ofstream::out | std::ofstream::app); fx << name << " = " << MRC << "\r\n"; fx.close(); } input.cpp: #include "Header.h" #include ofstream fio; void manual_input(int& N, float**& C, float**& b, float**& c1, float**& A2, float**& B2, float**& A1, float**& A, float**& b1) { //enter N cout << "Enter size (N): "; cin >> N; float NN = N; write_to_file1(fio, NN, N, 0, (char*)"N"); //generate Cij matrix(C, N); for (int i = 1; i <= N; i++) { for (int j = 1; j <= N; j++) { C[i-1][j-1] = (float)14 / (float)(i + pow(j,4)); } } write_to_file(fio, C, N, 0, 'M', (char*)"Cij"); //generate b (bi) -- ??????-???????? vector_Column(b, N); for (int i = 1; i <= N; i++) { if (i % 2 == 0) { b[i - 1][0] = (float)14 / (float)(pow(i,3)); } else { b[i - 1][0] = (float)1 / (float)(i+14); } } write_to_file(fio, b, N, 0, 'C', (char*)"bi"); //generate c1 -- ??????-????? vector_Column(c1, N); cout << "Vector Column c1 = " << endl; for (int j = 0; j < N; j++) { cout << "c1[" << j << "]="; cin >> c1[j][0]; } write_to_file(fio, c1, N, 0, 'C', (char*)"c1"); //generate A2 matrix(A2, N); cout << endl << "Matrix A2 = " << endl; for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { cout << "A2[" << i << "][" << j << "]="; cin >> A2[i][j]; } } write_to_file(fio, A2, N, 0, 'M', (char*)"A2"); //generate B2 matrix(B2, N); cout << "Matrix B2 = " << endl; for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { cout << "B2[" << i << "][" << j << "]="; cin >> B2[i][j]; } } write_to_file(fio, B2, N, 0, 'M', (char*)"B2"); //generate A1 matrix(A1, N); cout << "Matrix A1 = " << endl; for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { cout << "A1[" << i << "][" << j << "]="; cin >> A1[i][j]; } } write_to_file(fio, A1, N, 0, 'M', (char*)"A1"); //generate A matrix(A, N); cout << "Matrix A = " << endl; for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { cout << "A[" << i << "][" << j << "]="; cin >> A[i][j]; } } write_to_file(fio, A, N, 0, 'M', (char*)"A"); //generate b1 -- ??????-????? vector_Column(b1, N); cout << "Vector Column b1 = " << endl; for (int j = 0; j < N; j++) { cout << "b1[" << j << "]="; cin >> b1[j][0]; } write_to_file(fio, b1, N, 0, 'C', (char*)"b1"); cout << endl << "Thanks!" << endl; } //?????????? ???? (?????????) ????? void auto_input(int& N, float**& C, float**& b, float**& c1, float**& A2, float**& B2, float**& A1, float**& A, float**& b1) { //enter N cout << "Enter size (N): "; cin >> N; float NN = N; write_to_file1(fio, NN, N, 0, (char*)"N"); //generate Cij matrix(C, N); for (int i = 1; i <= N; i++) { for (int j = 1; j <= N; j++) { C[i - 1][j - 1] = (float)14 / (float)(i + pow(j, 4)); } } write_to_file(fio, C, N, 0, 'M', (char*)"Cij"); //generate b (bij) -- ??????-???????? vector_Column(b, N); for (int i = 1; i <= N; i++) { if (i % 2 == 0) { b[i - 1][0] = (float)14 / (float)(pow(i, 3)); } else { b[i - 1][0] = (float)1 / (float)(i + 14); } } write_to_file(fio, b, N, 0, 'C', (char*)"bi"); //generate c1 -- ??????-????? vector_Column(c1, N); for (int j = 0; j < N; j++) { c1[j][0] = rand() % 9 + 1; } write_to_file(fio, c1, N, 0, 'C', (char*)"c1"); //generate A2 matrix(A2, N); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { A2[i][j] = rand() % 9 + 1; } } write_to_file(fio, A2, N, 0, 'M', (char*)"A2"); //generate B2 matrix(B2, N); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { B2[i][j] = rand() % 9 + 1; } } write_to_file(fio, B2, N, 0, 'M', (char*)"B2"); //generate A1 matrix(A1, N); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { A1[i][j] = rand() % 9 + 1; } } write_to_file(fio, A1, N, 0, 'M', (char*)"A1"); //generate A matrix(A, N); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { A[i][j] = rand() % 29 + 1; } } write_to_file(fio, A, N, 0, 'M', (char*)"A");; //generate b1 -- ??????-????? vector_Column(b1, N); for (int j = 0; j < N; j++) { b1[j][0] = rand() % 9 + 1; } write_to_file(fio, b1, N, 0, 'C', (char*)"b1"); } main.cpp: #include "Header.h" #include //main int main(int argc, char* argv[]) { //????????? ?????? ??????????? ?????, ???? ???? ??????? remove("D:\\0.txt"); remove("D:\\1.txt"); remove("D:\\2.txt"); //??????? ???????? ???????? int procCnt = 0, procNumb; MPI_Init(&argc, &argv); /*START MPI